MOTION OF A PARTICLE 113
But if TI and r2 denote the distances of the particles from the axis of rotation, and P the period of revolution, then
Therefore -1 = ~2
ra2 r-i
gives the ratio of the masses of the particles as well as those of the given bodies.
MOTION OF A PARTICLE UNDER A CONSTANT FORCE.
102. Case I. Rectilinear Motion. — Suppose a particle of mass m to be acted upon by a force F, which is constant in direction as well as in magnitude. Then the force equation gives
dv F , /TA
or -T; = ~ = /. (I7)
dt m K '
Since both m and F are constant, /, the acceleration, is also constant. Integrating equation (I') once we obtain
v =ft+c,
where c is a constant to be determined by the initial conditions of the motion. Let the initial velocity be denoted by vQj then v= vQj when £=0, therefore c= VQ and
v = v* + ft. (1)
Substituting - for v in equation (1) and integrating,
Let s = 0, when t = 0 ; then c! = 0. Therefore
8 =^+!/*2. (2)
Eliminating t between equations (1) and (2) we get
v*=vo* + 2f8. (3)